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# What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ?

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]
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AbdurRakib wrote:
What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

OG Q 2017(Book Question: 68)

$$x^2$$ − $$4x$$ = $$96$$

Or, $$x^2$$ − $$4x$$ − $$96$$ = 0

Or, $$x^2$$ $$−12x$$ + $$8x$$ − $$96$$ = 0

Or, x ( x - 12 ) + 8 ( x - 12 ) = 0

Or x = 12 , -8

So , The larger of the 2 solutions must be (B) 12
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What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]
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Solving Quadratic equation $$x^2 − 4x = 96$$

$$x^2 - 4x - 96 = 0$$

$$x^2 - 12x - 8x - 96 = 0$$

x (x - 12) + 8 (x - 12) = 0

(x + 8) (x - 12)

x = 12, -8

x=12 is larger value

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]
AbdurRakib wrote:
What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

OG Q 2017(Book Question: 68)

$$x^2 − 4x = 96$$

Or, $$x^2 − 4x − 96 = 0$$

Or, $$x^2 − x ( 12 − 8 ) − 96 = 0$$

Or, $$x^2 − 12x + 8x − 96 = 0$$

Or, $$x ( x − 12 ) + 8( x − 12 ) = 0$$

So, $$x = 12$$ , $$− 8$$

Thus, larger of the 2 numbers is 12 , answer must be (B) 12
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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]
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AbdurRakib wrote:
What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

$$x^2 - 4x - 96 = 0$$
$$x^2 - 4x + 4 - 100 = 0$$
$$(x-2)^2 = 100$$
$$x-2 = 10$$ or $$x-2 = -10$$
roots are 12 and -8, with 12 being the larger. => Answer B
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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]
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The solution should be one of the roots of x^2−4x−96=0

Working from the answer choices, we can work backwards to see if we get an integer quotient by dividing 96 by the answer choice and then checking if we can get a -4 as the difference between the quotient and the answer choice.

Only B fits the scenarios as 96/12 = 8 and 12-8 is 4.
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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]
I have a question here. So in the equation given : x^2 - 4x =96 then x(x-4)=96 therefore x=96 or x-4=96 x=100
I know for the fact that this method is incorrect. But am not understanding why is it incorrect. can someone please help me
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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]
x^2−4x=96 => (x-12)*(x+8) = 0. > x = 12 or x = -8 => answer B
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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]
AbdurRakib wrote:
What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

x^2 - 4x - 96 = 0

(x + 8)(x - 12) = 0

x = -8 or x = 12

The larger of the two solutions is 12.

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]
Solving for quadratic is definitely the fastest route to an answer on this one but one could also simply test answer choices in a relatively fast manner as well w/o actually having to do much math (either start from E given we are looking for the "larger" of two solutions or use the optimal B/D approach)

E) 100^2 - 4(100) = 96 --> clearly doesn't work (recognize here that the x^2 needs to be a lot smaller)
D) 32^2 - 4(32) = 96 --> same rationale as above (x^2 still too big)
C) 16^2 - 4(16) = 96 --> x^2 still too big but getting closer...
B) 12^2 - 4(12) = 96 --> looks promising so do a quick check...144 - 48 = 96 --> correct answer choice

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]
AbdurRakib wrote:
What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

OG Q 2017(Book Question: 68)

$$x^2 − 4x - 96 = 0$$

Or, $$x^2 − 12x +8x - 96 = 0$$

Or, $$x(x - 12) +8( x - 12) = 0$$

Either x = -8 or x = 12, Thus Answer must be (B)
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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]
(x-12)(x+8)=0
x=12, x=-8
So larger solution is 12

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]
AbdurRakib wrote:
What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

OG Q 2017(Book Question: 68)

It might take a few attempts to know the two factors that once multiplied result in 96

We can choose from the answer choices

16 and 12 have a difference of 4 but will definitely have a multiple larger than 96.

So it is between 12 and 8 then it must be 12.

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]
AbdurRakib wrote:
What is the larger of the 2 solutions of the equation $$x^2$$ − 4x = 96 ?
A. 8
B. 12
C. 16
D. 32
E. 100

OG Q 2017(Book Question: 68)

x^2-12x*8x-96=0
(x-12)(x+8)=0
x = 12 or -8
Larger solution = 12

IMO B

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]
Hi all ,

Why can’t we solve this question as:
X(x-4) = 96
X = 96 , x = 100
Larger one is 100

Kindly guide

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Re: What is the larger of the 2 solutions of the equation x^2 − 4x = 96 ? [#permalink]
Instead of evaluating 96 for appropriate roots, one can also solve this by just rearranging the equation

x^2 +4-4x-4=96

(x-2)^2=100

(x-2)^2 - (10)^2 = 0 — this is a^2 - b^2

Hence we can straightaway get the two roots ie 12 and -8

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Re: What is the larger of the 2 solutions of the equation x^2 4x = 96 ? [#permalink]
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Re: What is the larger of the 2 solutions of the equation x^2 4x = 96 ? [#permalink]
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